Musicians, actors, artists and politicians across the world paid tribute to Ravi Shankar, described as "a national treasure" by the Indian prime minister, Manmohan Singh, as news spread of the musician's death in hospital near his home in California, aged 92.

Shankar, classically trained as an Indian musician but fascinated by other traditions, became as famous in the west as any rock star when he worked with groups such as the Beatles and the Rolling Stones, and played to vast audiences at legendary festivals like Monterey in 1967 and Woodstock in 1969.

Tributes came from classical and contemporary musicians, and from the Indian film industry for which he wrote many scores.

Manmohan Singh called him "a global ambassador of India's cultural heritage", and said an era had passed away with him. "The nation joins me to pay tributes to his unsurpassable genius, his art, and his humility."

The Bollywood actor Anupam Kher said: "Ravi Shankar's sitar played for all our souls", and the British Indian composer Nitin Sawhney described him as "my greatest childhood inspiration … I feel honoured to have worked with him." The composer AR Rahman said: "Indian classical music has lost its chief ambassador … May God bless his soul."

Film-maker Terry Gilliam, former member of the Monty Python team, wrote: "Ravi Shankar has left the building. 92 … a wonderful life", and tweeted a photograph taken at Monterey, commenting "he shines, as always".

Shankar's wife, Sukanya, and daughter and fellow musician Anoushka, who were by his side, announced his death "with heavy hearts" on his website. He had suffered breathing and heart problems over the past year, and underwent heart valve-replacement surgery last Thursday. The family said the surgery "could have given him a new lease of life", but added "though the surgery was successful, recovery proved too difficult".

His last live concert was only a few weeks ago, with Anoushka, on 4 November in Long Beach, California. His daughter Norah Jones is also an acclaimed singer.

One of his most famous collaborations was with the Beatles, through George Harrison's passion for the eastern musical tradition and determination to fuse it with western pop. When they first met, Shankar told Harrison his sitar playing on the track Norwegian Wood was "horrible", but they became close friends.

One of the first to tweet a tribute to him was Giles Martin, son of Sir George Martin, the record producer for the Beatles. "I bet George is happy to see him again," Martin said. "I'm very sad to hear of the death of Ravi Shankar," he said, "a beautiful, worldly man with warmth and talent."

The Canadian singer-songwriter KD Lang also called him a musical ambassador, and tweeted "May you have a swift and positive rebirth".

He was born in 1920, brought up in Benares, India and moved with his dancer brother to Paris. He first performed as a dancer, but then spent years studying the sitar. He won an Oscar nomination for his score for the film Gandhi, and was described by the late violinist Yehudi Menuhin, who also made several recordings with him, as a genius comparable to Mozart.

"He was legend of legends," Shivkumar Sharma, a santoor player who performed with Shankar, said in India, adding that before he took his country's music to the world, Indian classical music was not at all well known in the west.

"It's one of the biggest losses for the music world," said Kartik Seshadri, sitar player and music professor at the University of California. "There's nothing more to be said."